Question

Is this a binomial distribution? Explain.

Is this a binomial distribution? Explain.

Answer 1

For a binomial distribution, P(X = x) = C[n,x] x px x qn-x

X  =  0, P(X = 0)  =  C[n,0] x p0 x qn =  1 x 1 x qn =  0.064; one likely solution is n = 3 and q  = 0.4

 

Then p =  1-0.4  =  0.6

X  =  1, P(X = 1)  =  C[n,1] x p1 x qn-1 = n x p x qn-1 =  3 x 0.6 x 0.42 =  0.288

X  =  2, P(X = 2)  =  C[n,2] x p2 x qn-2 = n x (n-1) x p2 x qn-2 /2  =  3 x 0.62 x 0.4  =  0.432

X  =  3, P(X = 3)  =  C[n,3] x p3 x qn-3 = 1 x 0.63 x 0.40 =  0.216

 

We see that these values are matching with the values in the table.

 

So we can conclude that X follows a binomial distribution.

 

So we can conclude that X follows a binomial distribution